What's the meaning of 0 to 1 space in UV?
It is actually a coordinate system in percentage of image size.

A coordinate [0,0] corresponds the lower left corner, and [1,1] is the upper right corner (depending the the render engine/software.

It is made in such way that unwrapping is actually image size independent, so that if at a later time, you decide to use a larger image or an image with different dimensions the UV map still works and adapts (with distortions) to the new image format.

It is not a Boolean value nor is it limited to the 0~1 range, it is a float and can take on any value like -3.2, or 158.56.

The image will tile infinitely in X and Y axis repeating at every 1 unit, so for values bellow 0 or above 1 it will tile the image so that coordinate [2,2] will show the same part of the image as [1,1].